Answer: Anybody

Anybody – yes, anybody – may be living in the white house…!

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But if  it’s ‘The White House’ in question, then it must be the President of the United States or any of his family members or associates who lives with him. 🙂

Answer – The total number of buses met will be 9

Explanation-
EXCEPT for the FIRST 3 buses starting from either end, every other bus will meet another bus from the opposite site every 5 minutes.  This is because buses from both ends are moving simultaneously (covering equal distances, assuming buses moving at uniform speed).

Let us denote the distance covered in every minute as a point. i.e, considering one end of the route as Point 0, the other end will be Point 40. Consider a bus (Say, A) starting from point 0. The moment it starts, another bus B which had started 30 minutes earlier from the other end (Point 40) will be  already at 10 min. away (Point 10) from reaching  its destination. By the time bus A covers the first 5 points of its journey, the bus B also will have covered the same distance (from Point 10) and hence will meet bus A. By that time, yet another bus C (started from Point 40 following bus B)will be at 10 points away, and this bus will meet A in the next 5 minutes, just like bus B did. Thus, bus A will meet buses B, C… etc. every five minutes. This will continue till it reaches Point 40. Thus, the number of buses it meets en route will be 7. Counting the buses it meets at the starting point (the bus which had left Point 40, at 40 min. earlier) and at the terminating point (the bus which leaves Point 40 at the 40th minute of Bus A’s journey), the total number of buses met will be 9.

(For the first 3 buses starting at either end, this calculation will not apply, because, when the first bus starts from Point 0, there is no bus which had started earlier from Point 40 on the way to meet it at Points 5, 10 and 15. It will meet the first bus from the opposite end at Point 20 only. Thereafter, it will meet subsequent buses as described above. Similarly, when the 2nd bus leaves Point 0, there will be one bus at Point 30 (which was the first bus from Point 40, left 10 min, earlier) which will be the first bus it meets en route at Point 15. followed by subsequent buses as above.) 

Nowadays, repeat posts of same puzzle seems to be norm… 🙁

The newspaper man could be a viable suspect. The blood id dried means that the dead man was killed long time back. The milk was warm, means it was delivered recently – may be a few minutes ago. But the newspaper found on the porch was of Monday, which means that the last tine newspaper man made delivery was on Monday. Why didn’t he deliver on the next three days? (Probably) because he knew that the man is already dead. That makes him guilty of at least hiding a crime if not himself committing it.

(The newspaper man may argue that he didn’t deliver the papers after Monday because the (now-dead) man had told him (on Monday) that he was going out of town for a week or so. But the argument is weak, because, had the man planned any such trip, he would have informed the milkman also, and he also wouldn’t have made the delivery.)

It’s true that the man’s post-murder moves (avoiding fingerprints, discarding the knife etc.) are, of course, pretty ordinary in today’s world of crimes. Any criminal with the minimum level of sense would ensure the same. But then, changing / discarding the blood-stained clothes is at an even lower level of fundamentals of crime-hiding. Even in an era before the introduction of finger-print identification technology and other scientific investigation techniques, a blood-stained dress would have been nothing short of a loud announcement “Here comes a murderer…!”

It is true, as Yodha suggested, that people tend to get relaxed once they feel that the job is done, and may ignore some piece of evidence somewhere. (That’s mostly where the investigator can pick up and lead to the culprit).  But, for a criminal who is knowledgeable and thoughtful enough to such an extent that no fingerprints are left behind and the weapon is discarded never to be retrieved, forgetting to change the blood-stained clothes (which is tell-tale evidence) seems extremely unlikely.  Of course, there still is the possibility that he might change his dress, clean his footwear etc. and be satisfied with the efforts and hence be relaxed, thinking that he’s pulled off a perfect one, and yet end up caught because he missed a spot somewhere. But then, it is even more unlikely that such minute evidence will be noticed “as soon as he arrived” at the crime scene, as mentioned in the puzzle.

And, well, I’m also not fighting for or against any argument, but pointing out (fighting against?) the defect inherent in the puzzle – that it doesn’t have a fool-proof solution. Because of that fault, you need a ‘faulty assumption’ to solve it. (You can arrest the man alright, but, to get a guilty verdict, you need a water-tight case , which, unfortunately, is not there.)

The possibility of having blood on his clothes is also refutable, as the puzzle states that he was careful enough to avoid finger prints and to dispose off the knife in such a way that  it won’t be found. A criminal who is careful enough to wipe out incriminating evidence should have been hit by a massive bout of ‘short-term idiocy’ if he were to retain his blood-stained clothes, let alone going to the crime scene  in those tell-tale clothes.

In my ‘answer’, I mentioned ‘assumed‘ clue because it is only an assumption, and NOT necessarily be valid (as Yodha pointed out). And even in that “assumed” scenario, the case would still have a hole right in the middle.

This seems to be a refined version of a similar ‘wife murdered’ puzzle that had appeared here, the ‘key’  to the solution being the (assumed) clue that the Police had NOT informed the husband where the crime scene was located.  (If Police didn’t tell him, how could he have known the scene of crime, unless he himself was the killer?)

(I said ‘refined version’ because, in the original version, the fact that the husband himself had done the killing was not stated. However, the man does have an argument in his favour.)

Make it 10 TO 10 and think of TIME…!

– This nine fifty as time. That is 9:50 which is also 10 to 10.

Assuming that the colour “At” X feet is the colour AFTER the colour-change at that stage:

At 80 ft Kevin’s ball is red => the ball was purple at 60 ft; blue at 40 ft; green at 20 ft. => The ball was YELLOW at the beginning.
At 40 ft Larry’s ball is purple: Following the same line as above, it should have been GREEN in the beginning.
At 60 ft Charles’ ball is blue => The ball was originally BLUE itself.
At 100 ft Alex’s ball is purple => The original colour was PURPLE.

So, the ball left-behind must have been RED.

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Re-written after reading the puzzle again.